Quantitative Approximation Tricks

                       TRICKS TO CALCULATE FAST

How to approximate a square root when its not a perfect square?

Let’s say you want to find out square root of 144111

so 144111= 14000 approx

root(144000)= 10 root(1440)

35*35= 1225 so root(1440) is above 35

Now root(1440)= 1/2( 1440/35 + 35 )

= 1/2( 41 approx + 35)= 76/2= 38 approx; our answer = 38*10=380

Root (144111) actual value is 379.619

Let’s take another example:-

Say we need to approximate (275)^1/2

We know root(225) is 15

So from our method: our answer would be  1/2( 275/15 + 15)= 16.66

Trick is the closest you approximate initially; the more accurate will be the answer.

Finding cube root of any no:-

 Eg : to find d cube root of 39304

Step 1 : find d cube of d last digit I.e 4^3=64....

Take the last digit of this  no. I.e 4.  place it in the unit digit of the required cube root.

Step 2: cancel the last 3 digit from the no. I.e cancel 304.

Step 3: find the lowest nearest cube of first two digit or left no. Digits...nearest cube of 39 is 27 I.e 3^3

Hence the cube root is 34 for 39304.

 It is helpful for any perfect cube root no's.

 How to find sq. root of a Perfect sq:-

Let’s say we need to find root(6889)

Unit digit of our number is 9.  It could be because of 7*7 or 3*3 == > unit digit of our root could either be 7 or 9 .

Now cancel last two digits of our number i.e. 89,  we are left with 68.

Now find the nearest(smaller) root of 68== > 8  , Since 8*8= 64

This 8 will be tens digit of our root so we have 83 and 87 , now we need to conclude which one  is correct.

Trick is to multiply tens digit with +1 of it, and to see whether product is greater than or less than the number which we got after cancelling last two digits.

So 8*9= 72 since this 72 is greater than 68 , our unit digit would be smaller one. So ans= 83

Had 72 been smaller than 68 , our answer would have been 87.

Another example:-

Root(4761)  , apply same process

Unit digit: either 1 or 9.

Cancel last two, left with 47, closest root would be 6

So our number could be 61 or 69

Now 6*7= 42, since 42 is less than 47 , our unit digit would be 9.

So answer= 69.

Post Prepared By- Che Guevara Sir

Regards,

Classroom Team